Final answer:
The Doppler and transit methods are combined to determine the density of an exoplanet, helping to reveal whether the planet is rocky or gaseous by measuring its mass and size.
Step-by-step explanation:
The two exoplanet detection methods that are frequently combined to determine the density of an exoplanet are the Doppler method and the transit method. By using the Doppler method, astronomers can estimate the mass of the planet based on the gravitational influence it has on its host star, causing the star to wobble. The transit method, on the other hand, allows the measurement of the size or radius of a planet by analyzing the dip in brightness created when an exoplanet transits, or passes in front of its star. Together, these methods provide information on the mass and volume from which the average density (mass/volume) can be derived. This is crucial for understanding whether an exoplanet is rocky or gaseous.